It is with incredible sadness that we announce the passing of Stephen S. Shatz. Steve married Marilyn (nee Karpman) in December 1958. While married (divorced in 1977), they had two children, both of whom survive him – Geoffrey Shatz (married to Kristin) of Philadelphia and Aviva (fka Adria) Shatz of Fayetteville, AR. He is also survived by three grandchildren – Richard Gutierrez, Max Gutierrez, and Zane Wood.
An emeritus professor of mathematics, Steve died in July in Philadelphia, age 86. His passions and interests took in the full range of the sciences and arts. He was an avid eater who possessed advanced cooking skills and an expert knowledge of wine; he shared his love of astronomy with his friends and family; he found beauty in classical music – patronizing the Philadelphia Chamber Music Society and playing the flute – and loved learning to speak or read multiple languages, including but not limited to Italian, French, German, Russian and Yiddish; he even created his own translation of Dante’s ‘La Divina Comedia’.
Steve was known as a story-teller recounting adventures from his full life. From his Harvard years, he recounted when he drove hundreds of miles to a physics conference as an undergraduate with to-be Nobel prize winner Julian Schwinger and when he auditioned for and was accepted in a music performance class taught by Leonard Bernstein; from his travels as a mathematician, when a pesky rabbit almost foiled a lesson for his children about not eating poisonous mushrooms outside of Pisa, IT.
His life was nearly cut short in the early 1970s when he was diagnosed with cancer, likely stemming from an accident with a chemistry set in the 1950s. After five operations, the amputation of his right forearm, and chemotherapy, the cancer went into remission.
Born April 27, 1937, in Brooklyn, Steve attended P.S. 103 and then Montauk Junior High School before heading to Stuyvesant High School, the New York City honors high school. His parents were Nathan Shatz, an accountant, and Gussie Shatz, an opera singer and then homemaker. She would sing with Steve and his older brother Malcolm, imparting to them a love of opera.
Steve Shatz started at Harvard University in 1953, age 16, and earned an undergraduate degree in physics and then a Ph.D. in mathematics with a dissertation on The Cohomology of Artinian Group Schemes Over Local Fields under the direction of Professor John Torrence Tate Jr. Following the award of his Ph.D., in 1962, Steve was an instructor and then acting assistant professor at Stanford University through 1964. He then joined the faculty of the University of Pennsylvania, where he rose from assistant to associate to full professor from 1964 through 2005 before retiring on January 1, 2006. During that period, he chaired the Penn mathematics department from 1983 to 1986. Following retirement, Steve continued to conduct mathematical research and teach. During this period he developed a collaboration with Jean Gallier of the University of Pennsylvania Department of Computer and Information Science, producing manuscripts on algebra, algebraic geometry, and complex algebraic geometry.
His early papers in number theory broke ground in the investigation of cohomologies of sheaves for the flat topology of schemes invented by Grothendieck around 1960. In his Ph.D. dissertation published in the Annals of Math., he generalized Tate's duality theorem of Galois cohomologies of local fields, allowing the coefficients to be sheaves for the flat topology attached to arbitrary artinian commutative group schemes. In another Annals of Math. paper he proved that cohomological dimension of any non-perfect field of positive characteristic is infinite, a surprise, and also that the coefficient sheaves which caused troubles cannot be commutative group schemes of finite type over the given field.
In the middle 1970s his research direction made a slight turn, from arithmetic to algebraic geometry. In an influential paper he constructed a natural filtration for vector bundles on smooth projective varieties, generalizing the construction of Harder-Narasimhan for vector bundles on projective smooth algebraic curves. He also showed in an algebraic family of vector bundles, the convex polygon which encodes the discrete invariant attached to the filtration he constructed, always rises under specialization. This polygon defines a family of subvarieties on moduli spaces of vector bundles, commonly called Shatz filtration in honor of his contribution.
His charming book "Profinite groups, arithmetic, and geometry", published in 1972, is a stimulating introduction to arithmetic geometry. Based on a spring 1968 graduate course taught at Penn, it goes beyond the standard topics in Galois cohomology and local class field theory, to include topics such as Shafarevich's counter-example to the class field tower problem, Ax's counter-example to Artin's conjecture on forms and cohomological dimension, and (of course) duality theorems for finite commutative group schemes over local fields.
His career took him to conferences around the world, including Moscow in the 1960s and Bonn, Germany, as late as the 2000s. He was a visiting professor at the University of Pisa in Italy from 1966 to 1967, a member of the Mathematical Sciences Research Institute (now the Simons Laufer Mathematical Sciences Institute) in Berkeley, California, from 1986 to 1987, and a member of the Institute for Advanced Study in Princeton, New Jersey, in 1997.
A longtime member of the American Mathematical Society, Steve served as editor of the Transactions of the Society, on the Society’s Council, and on its Executive Committee of the Council. He is the author of numerous works in mathematics, including Profinite Groups, Arithmetic, and Geometry (Volume 67, Annals of Mathematical Studies, Princeton University Press, 1972), and a variety of journal articles.
In lieu of flowers, please make any donations in his honor to the Philadelphia Chamber Music Society.